CN114290327A - Six-axis robotic arm control system based on first-order variable gain ADRC - Google Patents

Abstract

The invention provides a six-axis mechanical arm control system based on a first-order variable gain ADRC, which comprises a first-order variable gain ADRC controller, wherein the first-order variable gain ADRC controller comprises: a linear tracking module; planning a path and a speed through an upper computer, outputting a given rotating speed and transmitting the rotating speed to a servo driving system; an expansion state observation module; all internal and external disturbances of the controlled system are considered as a whole, and a new state quantity, namely total disturbance (z), is expanded₂) And carrying out dynamic estimation and feedback compensation on the total disturbance; the variable gain fal function of the traditional ADRC is reserved, and the ESO is adopted to realize the estimation of total disturbance and the effect of replacing error integral feedback by feedback; a composite state error feedback module; in the SEF, the gain is composed of a nonlinear function fal, and the disturbance quantity obtained by the ESO is subjected to feedback compensation to counteract the influence of internal and external disturbance on the system.

Description

Six-axis robotic arm control system based on first-order variable gain ADRC

technical field

The invention relates to the technical field of robotic arm control, in particular to a six-axis robotic arm control system based on first-order variable gain ADRC.

Background technique

When the six-axis manipulator performs tasks such as grasping, handling, and docking, since the manipulator is composed of multiple joints, its own configuration and posture directly affect the load torque of the manipulator, and the load torque of the manipulator changes greatly. Due to the relatively fixed control parameters of traditional PID control, if the load torque increases, the control performance of the servo system will be degraded; in addition, the same set of PID parameters is also difficult to apply to the field of driving at full speed, especially the optimal PID parameters at high speed and low speed. require additional tuning.

The vector control system using ADRC controller has the advantages of adaptability to load change, robustness of parameters and strong anti-interference. Therefore, in order to ensure that the joint servo system has good dynamic and static performance in the full-speed domain when the external parameters in the system change, the ADRC controller is usually used instead of the ordinary PID controller in the speed loop.

The traditional nonlinear ADRC has the advantages of fast convergence speed and high steady-state accuracy. However, due to the existence of various nonlinear functions, it has high requirements for processor performance and many parameters are difficult to apply to practical occasions.

SUMMARY OF THE INVENTION

Aiming at the deficiencies of the prior art, the present invention provides a six-axis robotic arm control system based on the first-order variable gain ADRC.

The present invention realizes and solves the above-mentioned technical problems through the following technical means:

A six-axis robotic arm control system based on first-order variable gain ADRC includes a first-order variable-gain ADRC controller, and the first-order variable-gain ADRC controller includes:

Linear tracking module; the path and speed are planned by the host computer, and the given speed is output and transmitted to the servo drive system, as shown in the following formula

Expanded state observation module; considers all internal and external disturbances of the controlled system as one, expands a new state quantity-total disturbance (z ₂ ), and performs dynamic estimation and feedback compensation for the total disturbance;

Retaining the variable gain fal function of traditional ADRC, the simplified first-order ESO structural formula is

In the formula, z ₂ is the total disturbance observed, δ is 5Ts, Ts is the discrete step size of the system; β ₁ and β ₂ are the controller parameters; the fal function is the error nonlinear function, and its specific expression is

ESO is used to realize the estimation of total disturbance and feedback to replace the function of error integral feedback;

Composite state error feedback module;

In SEF the gain is composed of a nonlinear function fal whose structure is as follows

e ₁ =xz ₁

u ₀ =k _p fal(e ₁ ,α ₃ ,δ)

In the formula, u ₀ is the output control quantity, e1 is the error between the LT output tracking signal and the ESO feedback signal, kp is the gain coefficient, and α3 satisfies 0<α3<1;

Feedback compensation is performed on the disturbance amount obtained by ESO to offset the influence of internal and external disturbances on the system, that is,

u ₁ =u ₀ -z ₂

The final output of the controller is

u=u ₁ /b ₀

In the formula, b0 is the control amount gain, and in the servo drive system, u is the output q-axis given current.

The first-order variable gain ADRC control method includes the following steps:

S1 ADRC parameter initialization, S2 speed given quantity update, S3 state error feedback ESF, S4 feedback compensation, S5 output control quantity iq, S6 control object motor, S7 obtain real-time speed feedback, S8 observe disturbance quantity ESO; the S8 observes disturbance quantity ESO transmits data to S3 state error feedback ESF and S4 feedback compensation.

Based on the first-order nonlinear ADRC control speed tracking method based on the first-order variable-gain ADRC control method, the algorithm model was built in Matlab/simulink; the speed loop was tested by PI and ADRC controllers respectively, and the actual operation state of the manipulator was simulated. The speed is given as a planned acceleration line, and the load torque is changed during operation to observe whether the speed can quickly track the given speed.

As an improvement of the above technical solution, the comparison test includes: a load mutation comparison test and a load random disturbance comparison test.

Beneficial effects of the present invention:

A first-order variable gain ADRC is equivalent to a linearized special case of ADRC. On the basis of considering the actual application scenarios of the manipulator, the controller structure and algorithm complexity are simplified, and at the same time, the advantages of ADRC control accuracy and robustness are retained, making it especially suitable for the control accuracy of the six-axis manipulator. Requires higher servo drive system.

Using ESO to realize the estimation and feedback of total disturbance can replace the role of error integral feedback, so it can avoid the problems of slow system dynamic response, easy oscillation and integral saturation caused by error integral feedback.

Description of drawings

1 is a schematic flowchart of a six-axis robotic arm control system based on a first-order variable gain ADRC according to an embodiment of the present invention;

2 is a flow chart of the first-order variable gain ADRC program operation according to an embodiment of the present invention;

Fig. 3 is the load torque variation diagram according to the embodiment of the present invention;

Fig. 4 is the PMSM rotational speed response diagram according to the embodiment of the present invention;

FIG. 5 is a speed response diagram of a sudden load according to an embodiment of the present invention;

6 is a response diagram of a sudden unloading speed according to an embodiment of the present invention;

FIG. 7 is a load fluctuation diagram according to an embodiment of the present invention;

FIG. 8 is a speed response diagram when the load fluctuates according to the embodiment of the present invention;

FIG. 9 is a response diagram of the rotational speed at 180 rpm-250 rpm in FIG. 8 .

Detailed ways

In order to make the purposes, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention are described clearly and completely below. Obviously, the described embodiments are part of the embodiments of the present invention, but not all of them. Example. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

It should be noted that when an element is referred to as being "fixed to" another element, it can be directly on the other element or intervening elements may also be present. When an element is referred to as being "connected" to another element, it can be directly connected to the other element or intervening elements may also be present.

Example

As shown in FIG. 1 , the first-order variable-gain ADRC-based six-axis robotic arm control system in this embodiment includes a first-order variable-gain ADRC controller, and the first-order variable-gain ADRC controller mainly includes the following three modules:

(1) Linear Tracker (LT)

The rotation speed of the servo six-axis robot arm is mainly generated by the path and speed planning of the upper computer, and then sent to the servo drive system in real time through the protocol. In theory, there is no sudden change in speed. Therefore, in order to maximize the response speed of the controller, the traditional ADRC differentiator tracker is discarded, and the given speed is directly output, as shown in the following formula

(2 Extended State Observer (ESO)

As the core part of ADRC, ESO regards all internal and external disturbances of the controlled system as one, expands a new state quantity - total disturbance (z2), and uses a certain method to dynamically estimate and feedback the total disturbance. ESO does not need to know the exact model of the disturbance, so for the control system with large parameter changes, its robustness and anti-disturbance ability can be improved.

The variable gain fal function of traditional ADRC is retained. Since there is no differential component in the controller, the simplified first-order ESO structural formula is

In the formula, z2 is the total disturbance observed, δ can take a value of 5Ts, Ts is the discrete step size of the system; β1 and β2 are the controller parameters; the fal function is an error nonlinear function, with "small error large gain, large error. The characteristic of "small gain", its specific expression is

Using ESO to realize the estimation and feedback of total disturbance can replace the role of error integral feedback, so it can avoid the problems of slow system dynamic response, easy oscillation and integral saturation caused by error integral feedback.

(3) Composite State Error Feedback (SEF)

In general PID control, the proportional, integral and differential signals of the controller are linearly combined, and the control quantity u0 is output. In general, linear combination is not the optimal control method. Therefore, the gain in SEF is also composed of the nonlinear function fal, regardless of the differential signal, its structure is as follows

e ₁ =xz ₁

u ₀ =k _p fal(e ₁ ,α ₃ ,δ)

In the formula, e1 is the error between the LT output tracking and the ESO feedback signal, kp is the gain coefficient, and α3 satisfies 0<α3<1;

Finally, it is also necessary to perform feedback compensation on the disturbance amount estimated by ESO to offset the influence of internal and external disturbances on the system, that is,

u ₁ =u ₀ -z ₂

The final output of the controller is

u=u ₁ /b ₀

In the formula, b0 is the control amount gain, and in the servo drive system, u is the output q-axis given current.

To sum up, the structure of the first-order variable gain ADRC controller proposed in this patent is as follows:

The structure diagram of the first-order variable gain ADRC controller can be obtained from the above formula as shown in Figure 1; from the above structural formula and structure diagram, it can be seen that the first-order variable gain ADRC proposed in this patent is equivalent to the linearization special case of ADRC. On the basis of considering the actual application scenarios of the manipulator, the controller structure and algorithm complexity are simplified, and at the same time, the advantages of ADRC control accuracy and robustness are retained, making it especially suitable for the control accuracy of the six-axis manipulator. Requires higher servo drive system.

Example 2

As shown in Figure 2; the first-order variable gain ADRC control method includes the following steps:

S1 ADRC parameter initialization, S2 speed given quantity update, S3 state error feedback ESF, S4 feedback compensation, S5 output control quantity iq, S6 control object motor, S7 obtain real-time speed feedback, S8 observe disturbance quantity ESO; the S8 observes disturbance quantity ESO transmits data to S3 state error feedback ESF and S4 feedback compensation.

Example 3

In order to study the effectiveness of the first-order nonlinear ADRC control strategy and speed tracking performance improvement proposed in this patent, a first-order nonlinear ADRC control speed tracking method based on the first-order variable gain ADRC control method is proposed.

Build this algorithm model in Matlab/simulink. The speed loop is tested by PI and ADRC controllers respectively, and the speed is given as a planned acceleration line to simulate the actual operating state of the manipulator. Change the load torque during the operation and observe whether the speed can track quickly. given speed.

3.1 Load mutation comparison test

The change of the set load torque is shown in Figure 3;

Figures 4 to 6 are the speed response diagrams of the PMSM control system under ADRC and PI control respectively when the load is abruptly changed.

In the simulation, a load torque of 1N*m is applied at 1s, and unloaded at 2s. It can be seen that when loading, the motor speed drop under PI control reaches 60rpm, while the amplitude of the speed drop under ADRC control is greatly reduced to only 20rpm. Likewise, the amplitude of the motor speed controlled by LADRC during unloading is also significantly smaller than the speed change during PI control. Therefore, the dynamic performance of the motor control system using the ADRC controller proposed in this patent is obviously better than that of the PI control when the load suddenly changes.

3.2 Load random disturbance comparison test

Figure 7 shows the response diagram of motor speed and current under the condition of continuous load disturbance when the PMSM control system is running stably. In order to simulate the continuous disturbance of the load that may occur under the actual operating conditions of the manipulator, a disturbance signal of a certain frequency is added to the load torque of the motor in the simulation.

It can be seen from the speed changes in Figure 8 and Figure 9 that when the motor is running in a steady state, the speed fluctuation of PI control is relatively obvious, and the upper and lower amplitudes can reach up to 60rpm; the speed fluctuation of ADRC control is small, and the maximum amplitude is within 10rpm. . Therefore, the steady-state operation capability of ADRC proposed in this paper is better than that of PI control under load disturbance.

To sum up, under the same simulation experiment (same given and same parameters), compared with the PI controller, the drive system using the ADRC control strategy proposed in this patent can achieve fast speed tracking without overshoot, and has Better anti-load disturbance capability.

It should be noted that, in this document, if there are relational terms such as first and second, etc., it is only used to distinguish one entity or operation from another entity or operation, and does not necessarily require or imply these entities or operations There is no such actual relationship or order between them. Moreover, the terms "comprising", "comprising" or any other variation thereof are intended to encompass non-exclusive inclusion such that a process, method, article or device comprising a list of elements includes not only those elements, but also includes not explicitly listed or other elements inherent to such a process, method, article or apparatus. Without further limitation, an element qualified by the phrase "comprising a..." does not preclude the presence of additional identical elements in a process, method, article or apparatus that includes the element.

The above embodiments are only used to illustrate the technical solutions of the present invention, but not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: The recorded technical solutions are modified, or some technical features thereof are equivalently replaced; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims (4)

1. the six-axis manipulator control system based on first-order variable gain ADRC, is characterized in that: comprise first-order variable-gain ADRC controller, and described first-order variable-gain ADRC controller comprises: Linear tracking module; the path and speed are planned by the host computer, and the given speed is output and transmitted to the servo drive system, as shown in the following formula

Expanded state observation module; considers all internal and external disturbances of the controlled system as one, expands a new state quantity-total disturbance (z ₂ ), and performs dynamic estimation and feedback compensation for the total disturbance; Retaining the variable gain fal function of traditional ADRC, the simplified first-order ESO structural formula is

In the formula, z ₂ is the total disturbance observed, δ is 5Ts, Ts is the discrete step size of the system; β ₁ and β ₂ are the controller parameters; the fal function is the error nonlinear function, and its specific expression is

ESO is used to realize the estimation of total disturbance and feedback to replace the function of error integral feedback; Composite state error feedback module; In SEF the gain is composed of a nonlinear function fal whose structure is as follows e ₁ =xz ₁ u ₀ =k _p fal(e ₁ ,α ₃ ,δ) In the formula, u ₀ is the output control quantity, e1 is the error between the LT output tracking signal and the ESO feedback signal, kp is the gain coefficient, and α3 satisfies 0<α3<1; Feedback compensation is performed on the disturbance amount obtained by ESO to offset the influence of internal and external disturbances on the system, that is, u ₁ =u ₀ -z ₂ The final output of the controller is u=u ₁ /b ₀ In the formula, b0 is the control amount gain, and in the servo drive system, u is the output q-axis given current. 2. first-order variable gain ADRC control method according to claim 1, is characterized in that: comprise the following steps: S1 ADRC parameter initialization, S2 speed given quantity update, S3 state error feedback ESF, S4 feedback compensation, S5 output control quantity iq, S6 control object motor, S7 obtain real-time speed feedback, S8 observe disturbance quantity ESO; the S8 observes disturbance quantity ESO transmits data to S3 state error feedback ESF and S4 feedback compensation. 3. the first-order nonlinear ADRC control rotational speed tracking method based on the first-order variable gain ADRC control method according to claim 1, is characterized in that: in Matlab/simulink, set up algorithm model; Wherein rotational speed loop adopts PI, ADRC control respectively In order to simulate the actual operating state of the manipulator, the speed is given as a planned acceleration line, and the load torque is changed during the operation to observe whether the speed can quickly track the given speed. 4 . The first-order nonlinear ADRC control speed tracking method based on the first-order variable gain ADRC control method according to claim 3 , wherein the comparison test comprises: load mutation comparison test and load random disturbance comparison test. 5 .

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